How to Draw

DRAWING

and

SKETCHING OBJECTS

and

ENVIRONMENTS

from

YOUR IMAGINATION

HOW TO

DRAW

by $coH Robertson

w

ith

Thomas Bertling

designstudio

lpRESS

D

DEDICATION

This book is for those with a passion for drawing and learning.

Never stop!

BEYOND THIS BOOK:

It

[!]

.

Step-by-step videos are an integral part of the How To Draw educational experience! Use a smartphone or tablet to open a OR Reader app and scan this OR code. It links to the Design Studio Press image-recognition app needed to play the videos. Download the DSP app, scan Scott's photograph from page 008 and an introductory video will load.

All of the pages in this book that link to educational videos have a "play button" at the bottom, like this:

0

No smartphone or tablet? No worries.

Go to page 206, type in the URL on any computer to gain access to the entire links list.

Copyright © 2013 Design Studio Press. All Rights Reserved.

All text and artwork in this book are copyright © 2013 Scott Robertson, Thomas Bertling unless done by one of their former students or as noted throughout the book. No parts of this book may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, xerogrophy, and videography recording without written permission from the publisher, Design Studio Press.

Copy Editors: Melissa Kent, Erika G. Bertling, Heather K. Dennis, Jessica Hoffmann

I Graphic Design: Cecilia

Zo Published by Design Studio Press

Address: 8577 Higuera Street, Culver City, CA 90232

I Website: www.des

ignstudiopress.com

I E-mail:

info@designstudiopress.com

Printed in China

I

First Edition, November 2013 10 9 8 7 6 5 4 3 2 1

Library of Congress Control Number: 2013943344

I Hardcover ISBN·13:

978-193349273-5

I Paperback ISBN·13:

978-193349259-9 004

TABLE OF CONTENTS

INTRODUCTION

I PAGE 008

CHAPTER

01 Drawing Materials and Skills

I PAGE 010

012 Choosing Your Drawing Materials 013 Choosing Pens and Paper 014 The Craft of Drawing

015 Practicing Freehand Straight Lines 016 X-Y-Z Coordinate System

017 Practicing Freehand Smooth Curves 018 Practicing Freehand Ellipses

019 Drawing an Ellipse on the Minor Axis

CHAPTER

02 Perspective Terminology

I PAGE 020

022 Defining the Perspective by the Viewing Position 023 Cone of Vision -COV

024 Finding Vanishing Points on the Picture Plane

026 Physical Parallel Lines Converge to a Common Vanishing Point 027 Horizon Line Relative to Position

CHAPTER

03 Perspective Drawing Techniques

I PAGE 028

CHAPTER

04 Creating Grids

I PAGE 044

("1' 4;:'

S> _I

030 Division and Multiplication of Dimensions in Perspective 032 Multiplying and Dividing Rectangles

033 Dividing into Odd-Numbered Proportions 034 Mirroring in Perspective

036 Mirroring Tilted Planes

037 Mirroring Rotated, Tilted Planes 040 Mirroring 2D Curves

042 Mirroring a 2D Curve on a Tilted Surface

043 Mirroring 3D Curves in Perspective: The 2-Curve Combo

046 048 049 050 051 053 054 057 058 061 062 068

Perspective Grid Types Perspective Grid Construction

Diagonal Vanishing Point, Station Point Method

2-Point Grid Construction with Vanishing Points on the Page Rotated 2-Point Grids with Same-Sized Squares

Transferring Scale in Perspective

The Brewer Method: Constructing a Grid with Vanishing Points off the Page Creating a Grid of Squares, without Diagonal Vanishing Points

When to Use a Computer-Generated Underlay Other Benefits and Ways to Use an Underlay Not All Perspective Grids Are Created Equal Assembly and Exploded Views

CHAPTER

05 Ellipses and Rotations

I PAGE 070

~ I 072 Ellipse Basics and Terminology

073 Placing a Circle in Perspective or Drawing Ellipses 074 Creating a Cube Using Ellipses

074 Offsetting Ellipses

" , 075 Hinging and Rotating Flaps and Doors 076 Subdividing Ellipses

078 Shortcuts to Dividing Ellipses 079 Placing a Circle on a Sloped Surface

CHAPTER

06 Working with Volume

I PAGE 080

082 Planning Before Perspective

084 Orthographic Views, a.k.a. Orthogonal Views or Draft Views 085 Transferring a Side View into Perspective

086 Putting It All Together: X-Y-Z Section Drawing 088 Extending the Sections

089 2-Curve Combo 090 Cutting Volumes

092 Adding Radii and Fillets 093 Wrapping Graphics

094 Detailing and Sculpting Surfaces

096 More Tips for Modifying Complex Volumes 100 Contour Lines, Overlapping and Line Weight 102 X-Y-Z Section Drawing Applied

CHAPTER

07 Drawing Environments

I PAGE 104

108 Photo Underlay 110 Site Planning 112 Thumbnail Sketching 115 Non-Photo Blue, Then Ink 116 Sci-Fi Environment Step-by-Step

1 18 Warp That Grid with a Wide-Angle Lens! 120 Outdoor Environment Sketch Step-by-Step

CHAPTER

08 Drawing Aircraft

I PAGE 122

124 Airplane Anatomy 126 Visual Research

128 Drawing from Observation 130 Loose Concept Sketching 132 "Paper Plane" Ideation 133 "Paper Plane" Perspective Grid 137 Drawing a Paper Plane, Step-by-Step 142 Using a 3D Underlay

146 Final Airplane Drawing Step-by-Step

CHAPTER

09 Drawing Wheeled Vehicles

I PAGE

152

154 Visual Research

157 Have an Idea or a Goal Before Starting to Sketch 160 Some Basics on Vehicle Packaging and Architecture 164 Flexing Your Creativity

166 Grids, Grids, Grids!

169 Drawing a Side View in Perspective

170 Drawing a Stylized Side View in Perspective 174 Basic Body Sculpting

175 Drawing the Windshield and Greenhouse 176 Wheel Wells, Wheels and Tires in Perspective 178 Common Automotive Lines

180 Car Drawing Construction, Step-by-Step Grid 186 Vehicle Sketching with a Wide-Angle Lens

CHAPTER

10 Sketching Styles and Mediums

I PAGE

188

190 Ballpoint Pen

191 Copic Marker + Ballpoint Pen 192 Graphite Pencil

193 Colored Pencil

194 Pilot HI-TEC Pen on Newsprint 195 Copic Marker + Pilot HI-TEC Pen

196 Non-Photo Blue Colored Pencil + Marker + Brush Pen 197 Pentel Pocket Brush Pen

198 Copic Marker + Pen + Gouache 199 Gouache on Illustration Board 200 Toned Paper + Mixed Media 201 Digital: Sketchbook PRO

Glossary I PAGE 202

Index

I PAGE 203

Additional Resources

I PAGE 204

Video Links

I PAGE 206

Bios

I PAGE 207

Special Thanks

I PAGE 208

INTRODUCTION

Drawing is almost a magical power. It enables you to communicate in a different way than spoken or written language. Perspective drawing lets you convey how things work and how they look. You can inspire others with something as simple as a pen and a napkin!

When I created Design Studio Press, this is the first book I ever intended to write. Well DSP turned

10 years old this past March

. With 55 other books already in print, so much for Plan A! Finally, with the help of my good friend and longtime co-teacher, Thomas Bertling, I bring you the drawing know-how I've taught for over 1 8 years in my own workshops and at Art Center College of Design.

Organizing this book was like a sport where you train for years in order to compete at a high level for a few seconds. We combed through over a decade-and-a-half of demos and lectures to formulate the pages we now present to you.

Once you master these manageable perspective-drawing exercises, you will have the knowledge to sketch anything from your imagination, to think like a designer and draw things the world has never seen!

Books are great for looking at beautifully printed reproductions of original drawings and reading about the thoughts and methods behind those drawings, but video might be even better for step-by-step demonstrations. For that reason, many pages of this book link to online tutorials. Check out page

004

for a full explanation of how to use the Design Studio Press app.

Almost all of us drew when we were kids and some of us never stopped. While it takes practice to master the techniques in this book, it's worth the effort. Humans have been drawing for over 40,000 years so you're about to acquire one of the oldest forms of communication. Jump in and do the basic exercises at the beginning of this book with passion. As you master these ancient skills, pass along the knowledge and teach others the wonders of perspective drawing from their imagination.

Let's draw!

008

May 31

,

2013

Los Angeles, California

CHAPTER

DRAWING MATERIALS AND SKilLS

01

In this chapter you will learn about all the basic tools needed to get started with drawing. There are two categories: materials and skills.

It is important to know how to pick the right materials for the job at hand. As the topic and intent of the sketch changes, so will the materi-als needed. Quick loose sketches require a good flow of ink to paper and sometimes strokes should be very light to find "happy accidents" in the drawing. Tight drawings need a lot of attention. Optimally, one pen is used to generate varying thicknesses of lines. To achieve the best workflow, match different kinds

of

paper to different pens. When you find your favorite pen, make sure to buy several! Sometimes that beloved pen goes out of production way too fast.

Building up mechanical drawing skills is an important factor in cre-ating great drawings. It might seem simple, to draw a straight line, ellipse. or curve. But these skills must become ingrained in muscle memory so that concentration can be spent on construction versus thinking about how to create the lines in the construction. Also, these skills will help create clean drawings that can be done quickly and passed along the production line easily. Not having to use multiple tools will also speed up the drawing process.

Building muscle memory takes time and practice, so be patient! Take on the exercises one at a time, and soon your skills will improve.

CHOOSING YOUR DRAWING MATERIALS

In the beginning, a lot of money does not need to be spent on

materials. All that is really needed are pens, paper and a few basic tools. Brand names don't matter much, so let's get into the criteria for choosing materials.

Basic tools

1. Circle template

A circle template is quite useful to clean up circles, especially in side views. A compass is nice to have, but the circle template is faster to use. 2. Sweeps

The sweeps pictured above contain the most commonly sketched automotive curves. But don't rely on them to dictate your design. Always draw your lines freehand and then use the sweeps to clean them up.

3. Cotton pad, paper towel or tissue

To avoid ink globs on the page, dab the ballpoint pen frequently.

012 Scott Robertson

I Thomas

Bertling

I HOW TO DRAW

4. Equal spacing divider

An equal spacing divider is a super-handy tool that divides any distance into even segments.

5. Straightedge

Use a straightedge to construct grids for underlays. 6. Ellipse template set

Use ellipse templates to clean up ellipses. Alvin or Pickett are recommended brands since they work for most situations. A good set of ellipse guides is an investment, but worthwhile because it will last decades.

Pens

Pads

Paper

.

~

y

.c~ ~

CHOOSING PENS AND PAPER

Match the pen to the paper in order to create drawings with different line weights. Ideally, yau want to be able to draw both construction lines and contour lines without switching your drawing tool.

Ballpoint pens

When choosing a ballpoint pen, test it on the paper that you plan to use most frequently to see how much ink builds up on the tip as multiple lines are sketched. A pen that can sketch at least 10 lines without forming an ink glob on the tip is best.

No erasing!

Being able to erase is not an advantage in this style of drawing. There are so many intersecting construction lines that it is nearly impossible to erase anything without disrupting these valuable shortcuts that help to explain your drawing. Plus, erasing slows down the drawing process a lot.

So what can be done when erasing is not possible? Draw lightly. It's as simple as that. Sure, some lines might be incorrect, but you can clean up the drawing later with an overlay.

Refer to the last chapter of this book, page 188, for examples of combinations

of

materials used for various types of drawings. Choose a paper that works well with your preferred drawing tool. A rougher paper will be able to produce both thin and thick lines with faster flowing ballpoint pens.

Types of paper

Try many combinations of pens and paper until a favorite is found. Anything from cheap copier paper to specialty papers will work. There ore a couple of specialty papers that work well with markers as well as pens. Be aware that there are two sides to these papers: one side is waxed and the other is raw. Always draw on the raw side. The waxed side is there to prevent markers from bleeding through to the next page and it's terrible to draw on with markers.

Softness of the Drawing Surface

This is not referring to the paper itself, but how it is used. Drawing on a soft surface enables the best line quality. Do not work on a hard surface with a single piece of paper! Have at least 15 pages under a drawing to get the best line quality possible .

Working with underlays

Look for paper that is transparent enough so than an underlay can show through, but not so transparent that the table shows through when you present your drawings.

THE CRAFT OF DRAWING

Drawing requires full concentration! Initially you'll spend most of your energy on craftsmanship and construction and very little on design. The more craftsmanship and construction skills become muscle memory, the more design can become the focus. The first step in this

Set up a workspace

F _ ~ ___ ~ __ _ _~.J"fj

Learn to draw one straight line

1-

~==-

---"'--- ---"'---

---.---

-014 Scott Robertson

I Th

omas Bertling

I HOW TO DRAW

process is to practice the basic craft of drawing lines: straight lines, controlled curves and ellipses. This book has several good exercises for practicing these skills. As skills increase, the need to practice these exercises will diminish. Let's start with some warm-up drawings.

Clear the space! In order to stay focused, it's best to clear enough space and time to commit fully to the drawing. Have a clear work surface with tools at the ready. Flow will be broken when a pen or straightedge can't be found! The worst part is that the rhythm is lost for that drawing and what was clear ten minutes ago will take another ten minutes to understand again. Have a soft pad to draw on with at least 15 pieces of paper underneath the drawing for best line-weight results.

Being able to draw straight lines from point to point and in a grid is essential for all of the techniques in this book. These exercises may seem simple, but to do them well means burning through some paper to build the necessary muscle memory.

Let's look at the body mechanics that are necessary to achieve a consistently straight line. You only need to learn how to draw

one

straight line.

After that

rotate the paper to change the

line direction. Without this technique, keeping the paper in a fixed position would lead to having to learn how to draw an infinite number of straight lines. Draw with the whole arm! For long lines, use the elbow and shoulder joints; it's almost impossible to achieve this by only using the wrist. Draw slowly! Lines need to be repeatable and controlled. Draw each line once and do not trace the same line over and over again. Ghost the line! Go through the movement with the pen hovering above the paper. When the correct orientation is found, drop the pen on the paper and draw.

Is the line arching?

1. Muscle memory might have to be rewired when a line that feels straight while drawing results in an arch (red line).

2. The best way to counterbalance is to draw a line that feels like the opposite arch (green line).

3. After some practice the feeling of drawing a straight line and the result will match up (blue line).

PRACTICING FREEHAND STRAIGHT LINES

Drawing parallel lines

Start off with shorter lines, something in the 3-inch range, and work up to the full length of the paper_ Make sure to engage the entire arm and that lines are drawn consciously; they should be repeatable at the

--Aiming lines point to point

Below are two ways of practicing_ First, draw a couple of points on the page and connect them_ Remember to rotate the paper to orient one straight line that the body knows how to draw_ It's fine to overshoot the points slightly to improve flow_

Drawi ng boxes in perspective

A fun way to practice drawing straight lines is to draw boxes in l-point perspective. Draw a Horizon Line (HL) and choose a Vanishing Point (VP). Draw a rectangle and connect each corner to the VP. Draw another rectangle in the distance between these lines and you have a box!

HL VP

same length and spacing. Draw lightly. These are the fundamentals for drawing construction lines.

---

-

-

--

-The second exercise is to draw lines that meet in one point. Start to draw at any point outside of the center, draw a line through the center, and continue.

I /

/

I

-

--_.--- -~-\

Draw through

, which means to draw even the edges that would not be

seen, because they are behind the box. Draw the complete box with light construction lines, then darken the inside edges and the outlines of the box. The outlines should be darkest. Trace lines again and again to achieve different line weights.

- - --

- -

- -

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---=

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X-Y-Z COORDINATE SYSTEM

Sketching in perspective requires understanding the X-Y-Z coordinate

system. Each axis points toward a Vanishing Point. Each plane is perpendicular to its axis. Stay in control of your drawing by always knowing on which plane you are sketching. This system is used not

only to sketch boxes, but for all complex forms.

To draw a box where no side is perfectly perpendicular to the viewer,

2-point perspective is needed.

Drawing a box

In

2-Point perspective

HL

X Axis

- - ---. -

- - -

---

-1. Draw the Horizon Line (HL). Then draw

the front corner of a box. This establishes the X, Y and Z Axes.

HL LVP

-~ - - - -

-

- - -

----

-2. Extend the

X

Axis and the

Y

Axis lines from the bottom of the vertical, until they intersect the Horizon Line. The intersections of these lines create the Left Vanishing Point (LVP) and Right Vanishing Point (RVP) for the drawing.

LVP

3. Drow lines from the top of the vertical, to the Left and Right Vanishing Points. Then add two verticals at any distance.

""

X Axis

HL

LVP HL

-~~~----~

=

4. Close the box by drawing lines from the ,,~- :::-~ top of the two new verticals to the Left and , ---....

Right Vanishing Points. Add the resulting hidden vertical in the back.

LVP HL

-~---"

_"

----

----

-5. Darken the visible edges of the box. The drawing still shows the light construction lines. This is what it means to "draw through," which is very helpful to control

your drawings.

016 Scan Robertson

I

Thomas Bertling

I

HOW TO DRAW

- - -

.---l

Z Axis Y Plane X Plane

--

_Z

----

Plane Y Axis Y Axis RVP

- , -

-=4--RVP

- -- ---=-

~ =,.--~-:;;.-,."..-...

----RVP , __ 7 '1

,- --. - -::--

.--=--PRACTICING FREEHAND SMOOTH CURVES

Drawing curves through multiple points

Practice drawing accelerating curves through multiple pre-existing points. A smooth, graceful curve is optimal. This is done best by drawing the curve in segments, using the guide points as waypoints,

DO

DO NOT

Drawing requires not only straight lines, but curves too. There is a skill to drawing smooth, accelerating curves. When working in side view you determine how the curves flow; in perspective, the construction dictates how the curves flow and it can sometimes be surprising how radically some curves move in perspective.

not end points. Otherwise, the segments will have to be re-drawn multiple times and that causes fuzzy/hairy lines. Keep practicing curves to prevent this from happening.

DO

NOT

Place points that follow your intended de-sign, then create a smooth curve through those points. Rotate the page while drawing and use the natural curves your wrist and fingers draw. It's fine to draw the curve in segments; it's not necessary to draw it as one continuous line.

Create a curve with edges and corners. Avoid this by seeing the points as waypoints rather than endpoints.

Create a fuzzy line. Stay focused and methodical. Control the line as much as possible so that the task can be repeated over and over at a high quality.

PRACTICING FREEHAND ELLIPSES

Ellipses occur frequently. They are essentially circles in perspective, and some obvious ellipses are wheels and gauges. But they are also needed in constructions to rotate doors and objects. To become

Drawing an ellipse and adding the minor axis

1. Draw a freehand ellipse. Make sure to move the whole arm.

2. Draw with a light line. Later, the drawing can be cleaned up with an ellipse guide. Do not darken the lines too much by repeating the strokes. Even if you drew an incorrect ellipse, drawing over and over

it will only make it more obvious.

3. Check that the ellipse has no flat spots and is not lopsided.

4. Place the minor axis on the ellipse. The minor axis is the line that divides it in half across the narrow dimension of the ellipse making each half equal to the other. The minor axis plays an important role in placing the ellipse in perspective, so finding and controlling it is essential.

5. Double-check with an ellipse guide or fold the paper along the minor axis and check that the two halves line up on top of each other by holding the paper up to the light.

Fold ellipse along minor axis on top of itself.

018 - - - - Scott Robertson

I Thomas Bertling

I

HOW TO DRAW

0

comfortable placing ellipses, start by drawing a controlled ellipse. In later exercises, placing a circle in perspective, which becomes an ellipse, will be explained.

/

r

. /

. /

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'---.

....

Good line weight

Draw minor axis

--/ -

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(,,"---

.

---;--

---Cy

Too dark and too many lines

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)

Round

Clean up with Ellipse Template

~~

t

--·

\ I

DRAWING AN ELLIPSE ON THE MINOR AXIS

Now switch it up. Draw the minor axis first and then place the ellipse over

it. Align the hand correctly by rotating the paper to get the best angle.

Minor axis first ...

\

\

\

... then draw the ellipse

!

'-/

Make sure that the ellipse is symmetrical. Check that it is on axis. The minor axis needs to be centered and perpendicular to the drawn ellipse.

\

Perpendicular, but not symmetrical Ellipse is not perpendicular to axis

/

\

J

J

Drawing ellipses defined

by

the minor axis and width

Draw the minor axis, then a line to the left and the right of it. Make sure these outer lines are symmetrical or it will be impossible to draw ellipses that fit.

\

\

_'"

>

\

\

\

\

\

~

"

,

---\

Place the ellipses on the minor axis and match them to the width of the two additional lines. Vary the degree (how narrow or wide they are) as well.

\

-~

\ \ \

~,

\

\

~-

~.

"

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----020

---.

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- StabonpolOt 60 deg COV IS deg VP / 30degVP 60 deg VP

CHAPTER

PERSPECTIVE TERMINOLOGY

02

Explore this chapter to familiarize and refresh your knowledge of perspective terminology. The focus is on the terms and principles that are essential to navigate perspective drawings and to design objects and scenes from your imagination.

Remember, a true version of what is seen is not created, but rather emulated, since stereoscopic vision is not possible on paper. Humans have two eyes, which allows us to see in 3D. Drawing in perspective is a cheat, an approximation of how we see the world.

This chapter will explain the rules that exist to create the best illusion on paper. Once the rules have been mastered, it's okay to break them intentionally. However, if they are broken accidently, it can sabotage what you are trying to convey to the viewer. For example, imagine

you want someone to view your fantastic landscape and house as someplace they would want to live. Instead, a nagging question comes to their mind-something is odd and they cannot figure out what it is. This question is triggered by an inaccurate perspective in your drawing and should not have happened, since the goal was to talk about the project, not perspective. This was unintentional and ended up distracting the viewer from the goal.

Knowing the fundamental rules of perspective will allow you to join the discussion and exploration of perspective knowledge. There are many books that cover this terminology in depth, and doing additional research is encouraged. Join the community and start exploring your own questions and finding answers that allow for judging work and helping others.

DEFINING THE PERSPECTIVE BY THE VIEWING POSITION

Defining the viewing position is essential to controlling·the perspective drawing. Keep in mind that photography is being replicated in the drawings; therefore, it is essential to define where one is standing, the viewing direction, and the lens being used. This knowledge will apply

Defining Point of View -

(POV)

1. Ground Plane

Line of Sight

Station Point

2.

Picture Plane

022 Scott Robertson

I

Thomos Bertling

I

HOW TO DRAW

to the guessed perspective, the constructed perspective, and even to the computer-generated perspective. The rules need to be known so it becomes obvious when they are being broken.

Let's look at the following situation. A great picture of a building is taken with a camera and displayed. Another person wants to take the same shot when visiting the same location. In order for this to happen, the second photographer needs to know the location, viewing direction and the lens to use. This is the same information needed to create a drawing.

1.

Ground Plane

The position and direction where the photo was taken needs to be known. This could be on the street, on a bridge or on the sand at the beach. Whatever surface on which the photographer was standing or sitting is the ground plane. That's simple on Earth, but what about in outer space? In space it would still be considered as sitting or standing in a spaceship and this would determine the ground plane. What if the ship is removed from the equation? Then think

of

the ground plane as the extension of the soles of the feet.

Station Point· (SP)

Now that the ground plane is established, the location and height of the camera-or in the case

of

a drawing, the eye-needs to be disclosed. In a drawing this spot is called the Station Point. Think of the Station Point as a point in space that has no direction.

Line

of

Sight

The direction one is looking is the Line of Sight. The Line of Sight determines both the direction being looked and the incline.

In the graphic, the Line of Sight is parallel to the ground. This creates a 1- or 2- point perspective in which all physical vertical lines are represented by vertical lines in the drawing.

Tilting the line of sight (having it not be parallel to the ground) creates a 3-point perspective or even a 5-point perspective. For starters it is recommended to keep the Line of Sight parallel to the ground. This makes the construction considerably easier.

2. Picture Plane

-

(PP)

The Picture Plane is the surface on which images are recorded. Imagine the Picture Plane being a plate of glass that is pinned perpendicular to the Line

of

Sight.

It is time to capture the image. Close one eye and on the glass, start drawing what you see behind the plate of glass. The vision rays run from the eye to the object, passing through the picture plane. Record those transition points on the Picture Plane. This is perspective drawing.

How far is the Picture Plane from the Station Point? It doesn't matter for this construction. Pushing the Picture Plane away just creates a larger drawing, but will not change the proportions in the drawing itself. Historically, when the masters were really painting on glass, their arm length was the limiting distance factor.

1. Take a look at what was captured on the Picture Plane glass; specifically notice the squares on the ground. The squares closer to the box are less distorted than those that are closer to the viewer. The

captured image is correct with a high or low amount

of

distortion, but the closer squares are much harder to understand. They may be squares, but they look more like long rectangles.

Coming back to the camera analogy, it's time to choose the lens. This can be anything from wide to telephoto. The particular lens determines

how much of the area will be seen through the lens, which is what

is included in the drawing. It's assumed here that the camera would take a square picture as defined by the square picture plane on the previous page.

2. The optimal lens that creates an acceptable amount of distortion

is a 50mm lens. This translates into the drawing as a 60° Cone of Vision. How is this determined? Every lens has a degree of visible

area assigned to it and 60° is close to what is seen through a 50mm

lens. This cone is green in the drawings. A 90° Cone of Vision is

shown in red.

3. Going back to the drawing, the Cones of Vision have been added. There are two circles. The inner circle represents the 60° Cone of Vision and the outer circle the 90° Cone of Vision. It becomes clear that the area within the 60° Cone of Vision has less distortion than the area in the 90° Cone

of

Vision.

Cone of Vision degrees for different perspectives

When drawing, it's best to maximize the space on the poge and not draw objects that are too distorted. Here are guidelines for the Cone

of Vision degrees for different perspective constructions.

l-Point Linear Perspective Cone of Vision: 50'

l-point perspective is very prone to distortions. To avoid them

altogether, stay within a 50° Cone of Vision in drawings. Going even

as small as 40° is acceptable. Be aware that going too small will

flatten out the perspective like that of a telephoto lens.

2-Point Linear Perspective Cone of Vision: 60'

The Cone of Vision can be opened up more here. Be aware that around the edges, the distortion will increase, so it's best not to place any critical drawing elements near the edges. The 60° Cone of Vision

will be the go-to Cone of Vision for most drawings.

3-Point Linear Perspective Cone of Vision: 60'

Staying within the 60° Cone

of Vision is still recommended

.

5-Point Curvilinear Perspective Cone of Vision: open choice In 5-point perspective almost anything goes. Keep in mind that whatever is being drawn will be like a wide-angle-Iens photograph

at this point. To see examples of this jump ahead to page 047.

Perspectives can be created that allow more than the natural Field of View to be perceived. When this happens be extra mindful of the construction. Make sure to double-check all lines since instinct can easily lead to a wrong direction.

1.

2.

3.

CONE OF VISION - COV

Stron distortion

\

90' COY

60' COV

9~OV

FINDING VANISHING POINTS ON THE PICTURE PLANE

Diag.1

LVP HL

Diag.2

LVPk - = == _ _ HL Top view Picture Plane HL

---

---

---Diag.3

~

~

~

P

~

____

==========Fi~~==

~

F===

~

~

V~

f

----

HL

SP

024 Scott Robertson

I Thomas Bertli

ng

I

HOW TO DRAW

Let's emulate the "glass plate" experience on a piece of paper. Understanding where the Vanishing Points are, and how they relate to one another, makes it easier to build perspective grids.

1. When the parallel lines of the box are extended, each set converges to a Vanishing Point.

Letters used in the Drawings: SP Station Point HL CVP LVP RVP

45

VP Horizon Line

Center Vanishing Point Left Vanishing Point Right Vanishing Point

45" Vanishing Point, and other degrees

2.

To find the Vanishing Point for any set of parallel lines, use the top view and move one of the lines parallel until

it intersects the Station Point.

Next, find the point where that parallel line intersects the Horizon Line. This is its Vanishing Point.

3.

The next step is to abstract this construction to fewer lines

to be able to find any Vanishing Point in the future.

This drawing shows a combination of the top view and the Picture Plane. This is done to save space and is more efficient. It's called the Visual Ray Method for perspective drawings.

With both drawings combined, the two lines at the Station

Point have a relative angle of 90°. This angle of 90° is what locates the two Vanishing Points on the Horizon Line needed for the construction of obiects with 90° corners in

perspective.

Going from the Station Point directly to the Horizon Line will yield a perpendicular line. The point where this line intersects

with the Horizon Line is the Center Vanishing Point for this perspective construction.

4.

To find a new set of 90° Vanishing Points rotate the two

90° lines together. The center of rotation is at the Station Point. Any degree of rotation can be chosen. Here the 90° lines were rotated clockwise so that both intersect with the Horizon Line while still staying on the page.

5.

To place another box with 90° corners use the new set of Vanishing Points. Both boxes sit on the same ground plane and are rotated at different degrees relative to the viewer. A common error is to cause a rotated object to look like it's

floating above the ground or is tilted. This is caused by not matching the Vanishing Points to the same Cone

of

Vision.

6.

To find the degree of any Vanishing Point measure its deviation from the line that runs perpendicular to the Horizon Line and ends at the Station Point. To achieve a 90° box, the degrees of deviation of the Left and Right Vanishing Points will total 90'. Use them together as pairs and avoid mixing them with one another.

7.

Up to now in this example, random Vanishing Point pairs have been found. Now it is time now to find a matching pair of VPs that are more common. Other than 1-Point Perspective,

very common VP combinations are 75/ 15,

60/

30,

and 45/45. Take a second look at the 30° Vanishing Point. The edge of the

60

°

Cone of Vision runs through this Vanishing Point, while the center of the Cone of Vision is the Center Vanishing Point. 75

VP

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PHYSICAL PARALLEL LINES CONVERGE TO A COMMON VANISHING POINT

As a general rule, physical parallel lines converge to a common

Vanishing Point, but like anything else there are exceptions! In linear constructions for l-point and 2-point perspective these

exceptions are found. This is because l-point and 2-point perspective constructions are made more efficiently by not having

all physical parallel lines converge.

l-point perspective with some non-converging lines

2-point perspective with some non-converging lines

026 Scott Robertson

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HOW TO DRAW

In l-point perspective, there is only convergence into the depth

of

the drawing. Any lines that are parallel to the Picture Plane or perpendicular to the viewer will scale, but not converge.

In this drawing, neither the verticals nor the horizontals converge. In addition, all angled

lines that are on a plane parallel to the

Picture Plane do not converge either.

This makes using l-point perspective very

attractive, since it is quick to set up and use. There is only one direction of convergence and only one Vanishing Point to consider. Drawing by: Danny Gardner

View more of Danny's nice work at:

www.dannydraws.com

In 2-point perspective, all physical parallel lines converge except the verticals. The verticals stay vertical and do not converge. Keeping the verticals perpendicular to

the Horizon line makes it much easier

and faster to draw in 2-point perspective. The drawback is that the perspective can

quickly become distorted if the 60° Cone of Vision is abandoned. A 3-point perspective is needed to draw more dynamic views looking up or down.

HORIZON LINE RELATIVE TO POSITION

Standing higher or lower with the Line of Sight parallel to the ground

What happens to the Horizon Line when the Station Point is higher or lower? Let's review the set-up of these scenes. There is a side view (left) and the corresponding view of the blue Picture Plane (right). In the Cone of Vision, the Line of Sight is parallel to the ground at different heights. On the object are 3 height lines. Each

of

the lines corresponds with the height of the viewer's eyes.

Looking at these examples, notice that the corresponding height line is on the Horizon Line and flat, while the other height lines show convergence. Most important is that as the Station Point raises and lowers, so does the Horizon Line.

The changes shown affect how much of the object can fit into the Cone of Vision while remaining in 2-point perspective, with the verticals perpendicular to the Horizon Line.

1. Imagine standing on a large block and looking straight ahead. The corresponding height line is on the Horizon Line and level. Since the Cone of Vision moved up, less of the base of the object is seen.

2. Standing on the ground, the whole object can be seen in the Cone of Vision. The upper height line is converging,

while the middle one matches with the Horizon Line.

3. Standing in a hole, the corresponding height line matches the low Station Point. Now the upper part of the object is out of the Cone of Vision, but much more

of

the ground in front is visible.

1.

HL

2.

HL 3. HL PP

---

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PP

Tilting the head, or when the Line of Sight

IS

not parallel to the ground

When the head is tilted, the Line of Sight, Cone of Vision and Picture Plane move in tandem. In a linear perspective there will be 3-point perspective. Notice the verticals starting to converge. Then take a look at the height line! The line corresponding to viewing height is still on the Horizon Line, but the Horizon Line now has moved relative to the Cone of Vision and is not splitting it in half as it did when the Line of Sight was parallel to the ground.

4. Looking up, the verticals are converging and the base of the object is no longer seen.

5. Looking down, the verticals are converging toward the bottom and the top of the object is no longer seen.

4. HL 5. HL

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CHAPTER

PERSPECTIVE DRAWING TECHNIQUES

03

The drawing skills you acquired in the previous chapters are about to be put to good use! Construction techniques will be taught in this chapter that will provide a very powerful freehand sketching arsenal.

One of the goals of perspective drawing is to be able to find any point in space. Connecting two points creates a line and connecting multiple points can create a curve. Lines and curves are the building blocks to make objects of your imagination visible on the page.

The ability to multiply, divide and mirror lines and objects in perspective is essential. These basic techniques will be explained so you can start

to create more complex drawings.

Drawing lines lightly is essential, since a lot of lines will be created in a small area. Stick with a single pen and do not erase!

Why one pen?

Switching pens only slows you down and breaks your concentration.

Why no erasing?

The drawings become so dense with lines that erasing can't be done

without removing lines that are needed. Instead, draw lightly so that minor mistakes can be ignored. Work on the original drawing as long as possible. You can always create a clean overlay later.

DIVISION AND MULTIPLICATION OF DIMENSIONS IN PERSPECTIVE

Being able to divide and multiply dimensions in perspective is one of

the key building tools used to generate drawings. These rectangles provide the scaffolding to build upon.

No measuring required. This is a great advantage because it's quite labor-intensive to measure in perspective. On the left are orthographic constructions and on the right are perspective examples. The techniques that work in the orthographic view also work in perspective.

Dividing a rectangle

In

half,

In

perspective

I

030

1. First, define the rectangle. Make sure to stay within the Cone of Vision to avoid unexpected results.

2. Draw the diagonals by connecting the opposite corners. Draw lightly, since these lines should disappear in the final drawing.

3. To divide the rectangle vertically, draw a vertical line through the intersection point of the two diagonals.

In the orthographic view the rectangle is divided evenly.

In the perspective view, the rectangle is also divided evenly, but in perspective. The distance between the closer two lines is wider than the distance between the ones further away. This is called foreshortening.

4. This works equally well when dividing horizontally. Make sure that the vertical and horizontal lines follow the perspective grid.

5. Use this technique to find even subdivisions. This construction has been further divided into 1/4 as well as 1/16 (shaded pink).

--

---1-Duplicating a rectangle,

in

perspective

Reverse the technique used to divide a rectangle in order to duplicate any rectangle. This works great for building symmetrical objects, since the duplication line can be a centerline, too.

1. Define the rectangle and the direction to multiply toward. Since the height will stay the same, extend

the lines that go toward the multiplication direction.

2. Find the midpoint of the multiplication axis.

This point can be found with the diagonals or by

estimating the halfway point when the dividing line is horizontal or vertical.

3. Draw a diagonal that connects the far corner of the initial rectangle through the midpoint until it crosses the extended line.

4. Draw a parallel line from the intersection to find the boundary of the duplicated rectangle.

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TIP: Choose the shorter line (green) to draw! There are two possible diagonals but the shorter one is the better option, since shorter hand-drawn lines are more precise.

TIP: Multiplying in all directions is possible with this method.

MULTIPLYING AND DIVIDING RECTANGLES

Pay attention to your craft and make sure to draw light construction

lines. The rectangles can be observed automatically foreshortening. Rotate the page to get the best position for your arm to draw those straight lines. Eventually there will not be a need to draw all the lines;

some tick marks will suffice.

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1. Draw a lower and an upper line toward a common Vanishing Point.

2. Create a rectangle with two parallel lines.

3. Now that there is a base rectangle, multiply it either toward or away

from you. The rectangles will foreshorten automatically in perspective.

Multiplying and dividing boxes

More fun are the constructions where you stack boxes on top of one another.

Draw through!

Show the hidden edges of boxes where they are helpful. This is a way to double-check the constructions

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Watch out when making corrections. Avoid adding multiple lines to find the right one. It will only darken the lines and draw attention to the area of uncertainty. just draw one line and correct it by making an educated guess as to where the actual subdivision line should be. This will produce cleaner drawings and will be faster!

automatically. Should lines not meet at the expected intersection, go back and check where things started to misalign. Being deliberate about this will increase learning speed.

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DIVIDING INTO ODD-NUMBERED PROPORTIONS

1.

Define the plane.

2. Draw a line parallel to the Horizon Line, starting at the front edge of the plane. Divide this line into

5

equal segments.

3. Connect the last subdivision point to the end of the plane and continue the line to the Horizon Line. All lines parallel to this line will converge at this same Vanishing Point.

4. Draw parallel lines in perspective from each segment point to the new Vanishing Point.

5

.

Draw vertical lines at each of the intersection points to transfer the subdivisions.

You have divided a rectangle into 5 equal sections, in perspective.

What happens if there is a need to divide by 3 or more? This can be accomplished with a very fundamental technique of transferring a proportion into perspective. In this example let's subdivide a rectangle into

5

equal units.

Perspective view

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MIRRORING IN PERSPECTIVE

It is essential to be able to mirror elements to draw symmetrical objects. To mirror any point in perspective, use one of these rectangle multiplication techniques. These techniques are very versatile and can be mixed and matched.

Mirroring horizontal planes

1. Draw a rectangle and a perpendicular mirror plane. Extend the width lines of the rectangle toward the mirror plane until they intersect it. Draw diagonals in the rectangle to find its midpoint, and draw a line from that point, in perspective, to the mirror plane.

e-

-3. Mirror the far line by using the multiplication technique.

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034 Scott Robertson

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I HOW TO DRAW

2. Use the mirror point to mirror the closer line to the mirror plane with the multiplication technique, then move on to the far line.

4. A mirrored plane has now been created. This technique can be applied for other parallel plane constructions. Remember this is all based on the multiplication technique!

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1. Here, the same technique is used to mirror

a vertical plane. Draw diagonals to find the midpoint of the mirror plane.

Mirroring offset planes

-2. Extend the width dimensions

of

the rectangle for the expected position of the

mirrored rectangle and find the centerpoint

for mirroring.

Mirroring vert

i

cal planes

3. Complete the construction with the diagonals and find the height of the

mirrored rectangle. Darken the lines of the

resulting rectangle.

1. Set up a plane that hovers above the ground or mirror plane.

Extend the lines at each of the corners in the mirror direction.

2. Mirror the front line by using the multiplication technique.

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3. Complete the plane by following the perspective grid and using the vertical lines to define the size of the plane.

4. Darken the outer edges.

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MIRRORING TILTED PLANES

Mirroring tilted planes uses the same technique of multiplying

rectangles. These side-by-side examples illustrate this principle. They are separate constructions, mirroring different tilted planes.

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1. Set up a tilted plane and the plane to be used as a mirror. Use a perspective grid to determine where both planes are located in space, relative to each other. This is essential

to stay clear on the construction.

2. Choose a point (A) to mirror. Extend the

tilted plane line (red line) and the mirror

plane line to mark the intersection point (B).

Drop a vertical line from the top of the tilted

plane to the ground plane

(C)

,

if it is not already there as part of the construction.

3. Use the multiplication technique to mirror

point A, to create point D.

4. Draw a line between points Band D.

The angle of the plane has now been

mirrored in perspective.

5. To finish drawing, use the perspective

grid guidelines going to the LVP to transfer a few more mirrored points (E and

Fl.

Connect these points to create the mirrored planes.

Scott Robertson

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Thomos Bertling

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HOW TO DRAW

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Sometimes drawings require dealing with planes that have a more complex position in space. Three points define a plane. To create a rectangle, the fourth point needs to sit on the same plane. This is

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----MIRRORING ROTATED, TILTED PLANES

easy to forget when drawing. Things can be sketched that are not physically possible. Check out M. C. Escher; he did it on purpose.

1 . Take a look at all four points of the tilted and rotated plane. Each of the points moves

deeper into perspective. Only two 2-point sets match up in height, but none match up

in depth and width.

2. Take the top-front point and mirror it across the mirror plane. Use the rectangle duplication technique.

3. Extend the tilted centerline and cross it with the extended tilted front edge.

4. Connect the intersection point with the already mirrored top-front corner.

5. Draw a line from the lower-front corner,

perpendicular in perspective to the mirror plane. Where it intersects the line from step

4 is the lower-front corner, mirrored.

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6. Now find the mirrored line on the ground.

Start in the lower-front corner and extend the

line on the ground until it intersects with the

mirror plane.

9. Find the endpoint of the upper edge

by extending the upper line in the back

of the construction.

1 1. Darken the edges

of

the planes.

7. Clip the line at the correct length by extending the line that is perpendicular to

the mirror plane and runs to the lower back

edge of the rectangle. This will cross the mirrored directional line and determine the length of the line on the ground.

10. Connect the open edges. You have

mirrored a plane that was tilted and rotated.

f

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038 Scott Robertson

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HOW TO DRAW

o

8. Repeat the same technique to find the upper edge direction and length.

Practicing these constructions raises awareness of patterns in the environment. Mirroring planes seems like an abstract exercise, but becomes very applicable as soon as you want to draw a car or a jet plane. There are a lot of multiplications in buildings too. In the photo,

the green construction lines run through the same points on multiple arches, which is a big timesaver. After finishing this chapter and learning about mirroring curves, take another look at this construction and there will be increased understanding.

MIRRORING 20 CURVES

Mirroring curves gives you control over organic surfaces. The base construction still relies on straight lines and perspective control. 2D curves are by definition on a plane. This plane can be tilted in 3D space.

Orthographic View

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HOW TO DRAW

First, define the plane on which the 2D curve is to be drawn. Box the plane into a rectangle and mirror this rectangle in the direction you want to mirror the curve .

Technique 1 :

1. Draw a V that is mirrored by using the corners of the rectangle and a common point on the centerline. 2. Draw a horizontal line from the intersection of the curve and diagonal, until it crosses the mirrored diagonal.

3. Transfer multiple points that will define the mirrored curve.

Technique 2:

Instead of drawing the diagonals to the corners of the rectangle, use the middle line that was generated by the original construction.

Technique 3:

1.

In this case decide which point to mirror on the curve (A).

2. Place a diagonal through that point to the centerline (B).

3. Add a horizontal line from points

C to D.

4. Mirror the diagonal line by drawing a line from B to D.

5. Add an additional horizontal line from the intersection points A to E.

Perspective View

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The rectangle duplication method

works here, too.

1. Define the point to mirror. 2. Draw a vertical and a horizontal line to create a rectangle.

3. Duplicate the rectangle to use as the base to mirror the point.

All Techniques Combined:

Here all methods have been combined to show how the points define the mirrored curve.

Which method should be chosen?

Pick the technique that provides the most points in the most efficient way, and combine techniques as needed .

. \

MIRRORING A 20 CURVE ON A TILTED SURFACE

042

1 . Define the tilted surface. Draw a curve on it.

3. Draw a diagonal

on both planes, so that the nearside diagonal

intersects the curve.

5. Draw a line from the intersection of the

centerline of the tilted plane to the curve. Transfer the information to the mirrored plane.

Scott Robertson

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Thomas Bertling

I HOW TO DRAW

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2. Use the plane mirroring technique to create the mirrored plane on which

the mirrored curve will sit.

4. Draw a line in the perspective grid direction from the intersection point until it crosses the mirrored diagonal. There are now three points for the mirrored curve: the start point, the endpoint and the new point just created.

6. Repeat the previous step, but this time use the horizontal middle line to find the intersection with

the curve.

These lines can be moved to wherever the transfer point is desired.

MIRRORING 3D CURVES IN PERSPECTIVE: THE

2-CURVE

COMBO

1. Build a full construction of the 3D curve. This is done with the

2-curve combo technique on page 089. Knowing where the line is in

space is essential for these drawings.

Q

3. Repeat this process for the rest of the points on the curve. Mirroring some

strategic points instead of all points is an option here, but in the beginning

add enough points so that the curve can be found with confidence.

5. Once the curve is mirrored it's time to find the footprint

of

the curve. Drop in the verticals until they cross with the extended lines on the ground.

2. Start with mirroring the starting point of your curve. The rectangle

is being duplicated, but skip the vertical line since the vertical is not

essential to the goal. Guessing the mirror point is possible here since there is very little perspective foreshortening in the vertical line.

4. Connect the points to find the mirrored curve and draw a smooth

line. If one point seems off; just compensate as needed.

6. Now there are two mirrored curves: one 3D curve (green) and one

flat curve (black). This technique creates a 3D volume at the same time

it mirrors the curve.

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Scott Robertson

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HOW TO DRAW

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---CHAPTER

CREATING

GRIDS

04

This chapter focuses on constructing and understanding grids.

The most commonly used perspectives have Vanishing Points that are off the page. Grids help aim lines toward those Vanishing Points.

Grids come in very handy when working with complex drawings and multiple objects. Understanding the basics of grids is important in being able to decide how to use photographs or computer-generated underlays.

When working without a grid, a lot of effort is spent trying to aim lines in the correct direction, with the worst part being not knowing whether or not the lines were on target. Having a basic grid alleviates this problem by aiming the lines. This makes it possible to concentrate on construction and later, on design, as drawing becomes more automated.

Eventually you can stop using grids for the easy things, but for difficult constructions with hinged parts, rotated elements, and multiple views of the same object, a base grid is very helpful.

Grids can be reused often since they are not drawn on, but rather placed under the drawings. A grid used as an underlay should be as precise as possible, and it's important to choose the most effective way to create it, based on its particular use. It can be hand-drawn with a straightedge, drawn in 2D software or generated by 3D software. Creating a process and updating it on a regular basis is part of being a designer and a problem solver.

PERSPECTIVE GRID TYPES

Let's look at a couple types of perspective grids that are often

encountered and that are useful for drawing. It's important when

choosing a grid to consider the purpose of the final drawing.

Some grids are better for the ideation of an environment than for

l-Point

Perspective Drawings

The l-point perspective grid is excellent

for ideation and adding perspective to a side-view sketch. It's easy to generate and the perspective from left to right and up to

down is easy to control. This makes it simple

to transfer proportions, since they are

one-to-one and just scale smaller when going

deeper into the perspective. However, it

is more difficult to control the depth of an

object in this perspective. The depth can

become very shallow and the perspective

can compress a lot as it gets closer to the

Horizon Line.

2-Point Perspective Drawings

The 2-point perspective grid is one of the most commonly used grids.

The grid changes with the orientation of the object to the viewer.

Having an individual object in 2-point perspective is rather basic,

but when it comes to having two or more rotated objects on the

same surface things become more tricky. A 2-point perspective gives

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HOW TO DRAW

products. To make things more complicated, it also depends on the

user's comfort level. There is no absolute right or wrong. These are

guidelines; not the law!

the viewer a good idea of the orientation in space of the objects

being shown. The effect is similar in a 3-point perspective, but the

drawing complexity increases since the verticals are not parallel to

one another. Having the verticals perpendicular to the Horizon Line

in this perspective grid makes drawing much easier.